A fast iterative algorithm is presented for the numerical solution of large linear systems that are encountered in multiparticle Stokes flows. It is applicable to solid particles of arbitrary shape, and finds the translation and rotation velocities when total forces and torques acting on these particles are given (mobility problems). An exact result for the stresslet is also given. The method is based on recently developed boundary integralequations, “the canonical equations for mobility and resistance problems.” These are well‐posed Fredholm equations of the second kind, for mobility problems or problems with arbitrary velocity boundary conditions. They are modified for the direct iterative solution of mobility problems, leading to fast numerical computations. For a single sphere the iteration operator is spectrally decomposed analytically. The convergence rate of the iterations is deduced, and supporting numerical observations are presented. Fast rate of convergence is numerically observed for multisphere problems even at small separations. Simulations in polymeric and suspension rheology and protein chemistry are envisioned as potential applications. Numerous solutions are needed when simulating such systems over some period of time. With nearly equal consecutive boundary configurations, each previous solution provides a good initial guess for the next iterative solution.

Sleep is a period of rest that is essential for functional learning ability, mental health, and even the performance of normal activities. Insomnia, sleep apnea, and restless legs are all examples of sleep-related issues that are growing more widespread. When appropriately analyzed, the recording of bio-electric signals, such as the Electroencephalogram, can tell how well we sleep. Improved analyses are possible due to recent improvements in machine learning and feature extraction, and they are commonly referred to as automatic sleep analysis to distinguish them from sleep data analysis by a human sleep expert. This study outlines a Systematic Literature Review and the results it provided to assess the present state-of-the-art in automatic analysis of sleep data. A search string was organized according to the PICO (Population, Intervention, Comparison, and Outcome) strategy in order to determine what machine learning and feature extraction approaches are used to generate an Automatic Sleep Scoring System. The American Academy of Sleep Medicine and Rechtschaffen & Kales are the two main scoring standards used in contemporary research, according to the report. Other types of sensors, such as Electrooculography, are employed in addition to Electroencephalography to automatically score sleep. Furthermore, the existing research on parameter tuning for machine learning models that was examined proved to be incomplete. Based on our findings, different sleep scoring standards, as well as numerous feature extraction and machine learning algorithms with parameter tuning, have a high potential for developing a reliable and robust automatic sleep scoring system for supporting physicians. In the context of the sleep scoring problem, there are evident gaps that need to be investigated in terms of automatic feature engineering techniques and parameter tuning in machine learning algorithms.